How is simulated annealing better than hill climbing methods?
In the least technical, most intuitive way possible: Simulated Annealing can be considered as a modification of Hill Climbing (or Hill Descent). Hill Climbing/Descent attempts to reach an optimum value by checking if its current state has the best cost/score in its neighborhood, this makes it prone to getting stuck in local optima.

Simulated Annealing attempts to overcome this problem by choosing a "bad" move every once in a while. The probability of choosing of a "bad" move decreases as time moves on, and eventually, Simulated Annealing becomes Hill Climbing/Descent.

If configured correctly, and under certain conditions, Simulated Annealing can guarantee finding the global optimum, whereas such a guarantee is available to Hill Climbing/Descent iff the all local optima in the search space have equal scores/costs.

For more, go through Wolfram Mathworld's entry here.